If you can’t explain something in simple terms, you don’t understand it
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"Hell, if I could explain it to the average person, it wouldn't have been worth the Nobel prize." [1]
Showing a limitation of the maxim or Feynman's hubris?
At least as good as math (and capturing the objective complexity better I think) is a working program. "What I can't program, I don't understand."
When people ask for a simple explanation, they usually expect it to be easy for them too, because we all want simple and easy at the same time, even though only one of those is objective. If your reply to "how do magnets work?" is to start by writing down Maxwell's equations, you're gonna get crap for it, but someone who uses the fake rubber band analogy will be well received. But who really understands magnetism better?
Trying to explain a concept in "simple terms" forces you to view it in terms of its connection to other, well-known phenomena.
At this point it's turtles all the way down.
You have to arbitrarily decide where to end: typical 5-year-old, typical high-school student, typical math professor.
What people mean by "simple terms" is "simple terms that I understand".
That's what it looks like if you only look at the formula. (And why I'd say that formulas are not an "objectively simple way of expressing something*)
If you can somehow keep in mind what the formula is supposed to represent, the operations on characters will let you find some insight about that thing and will stop standing only for itself.
Also, mathematical formulas are essentially a different language. If people don't speak it, then it's a moot point.
> Feynman was also quoted as saying:
> I think I can safely say that nobody understands quantum mechanics.
http://www.sciencealert.com/watch-richard-feynman-on-why-he-...
As you say, informal explanations are great for understanding and bringing clarity, a lot of the time they're just used to help expand the unfamiliar math, but also a lot of the time they trade off precision, conciseness, or accuracy. At worst they complicate things with twists and relations in the informal explanation that don't exist in the real deal. Sometimes that might be helpful in the same way technically unrelated mnemonics are but it's important to point them out.
The conflation of simple, easy, concise, precise, clear, intuitive.. is the root of the issue when discussing what makes a good explanation.
This, of course, does not hold for the inverse of 'what I can program, I do understand'.
The most useful meaning is "Have a consistent and reliable model for."
The code implements a model. Of course you can implement a very bad model as easily as a consistent and reliable model.
Obviously, if you use the "hairy" physics etc terms, then the layman wont understand your explanation, because he is not familiar with them.
I've seen people from my domain making ridiculous, inaccurate analogies and oversimplify to hide the inherent challenges that a task usually involves. And they get away with that because they aren't the ones actually building the product. They just have to sell it. And the one's they are selling to aren't/won't be using the product either, they will tell someone else to use it.
QED does explain quantum electrodynamics without any calculus or other math (for example, he uses imaginary clocks as a way to explain wave interference), but I think if the average person read it they wouldn't walk away with even a partial understanding of it.
This is also true for literature, poetry, non-analytical philosophy etc. And there the challenges are not about the complexity of the subject, but about its subtlety, and how one needs historical context and/or certain life experiences (or even proclivities) to be able to grasp a particular piece of work.
Taking mathematics as the operative example. A lot of deep theorems are trivial when you fully understand all relevant definitions. These proves cannot be stated 'in simple terms' because it took a stack of non-simple definitions to even formulate such a theorem.
Explaining the entirety of the stack gets hard when the stack gets deep. For example, a lot of math gets really hard to explain when the concept of the real numbers being 'uncountably infinite' whilst the rationals are 'countably infinite' isn't obvious.
A lot of deep theorems comes down to properly choosing the definitions so that the theorems are true.
But seriously, if you can't explain what a complex-valued "probability" is to a layman, apparently you don't understand quantum mechanics?
(Highly recommend the whole Feynman series, which is excerpted from an interview video called The Pleasure of Finding Things Out, which is also spectacular)
[1] http://www.nobelprize.org/nobel_prizes/physics/laureates/196...
She'll still have no idea what an interface actually is, but she'll have a good grasp of the concept.
If you rehash it in smaller words, just by information density alone, aren't you guaranteed to be losing some detail?
The notion here is that educating beginners about a subject is different from communication between experts. Yes, experts use jargon because it is more efficient. But, the notion here is that if you truly understand something, you should be able to find a way to explain it to a non-expert, building up from words and concepts they already understand. And, further, if you can't do that, then perhaps your understanding is not as deep as you thought it was.
Was he referring to the Z state? If so, it's not really ternary logic but rather a "no result" state for cases where there is a control signal involved (e.g., in a tri-state buffer).
Even more non-binary things happen inside DRAM and flash memory.
DRAM is analog-based due to the fact that the core memory unit is a capacitor, so it can't be ternary (not digital). I might agree with flash though.
Algebra and calculus were one bleeding edge research that only the elite understood, now kids are learning it in middle school.
Yes, but knowing which information you can lose is why it is said that you don't understand it until you can explain it. Explaining it in simple terms forces you to over-simplify, and then you have to pick which information is important and which isn't...and doing that requires a deep understanding of the subject (and your audience).
Of course, but when explaining something to another person, one should strive to optimize for being understood, not for the highest information density.
If you skip out the part of the analogy where you actually return to the complex terminology you're simplifying, you haven't produced understanding - you've only made a just-so story which is a reflection of the reality, not a justification for it.
> If you skip out the part of the analogy where you actually return to the complex terminology you're simplifying, you haven't produced understanding
Billions of people know what a telephone does and how to use one without understanding τῆλε ("tele-", distant) and φωνή ("phone", voice, talk, language). They all get the concept and nobody would argue that they need to understand the terminology as well.
Or: I can teach you to play chess without teaching a single chess-specific term. Yes, other players will laugh at you when you call the pawns "smurfs", but when you understand how to handle your smurf-army, opponents will stop laughing after hearing you announcing "death by smurf-supported horse in 2 turns". (Though they'll definitely hate you for calling a knight a horse ;).
But that doesn't remove the terminology, it only changes it. You can understand chess equally well in English, French, or Lebanese, because the syntax isn't as important as the semantics. You can't teach me chess without talking about the idea of a "piece", no matter what you end up calling it. There has to be some common groundwork.
>Billions of people know what a telephone does and how to use one without understanding τῆλε ("tele-", distant) and φωνή ("phone", voice, talk, language). They all get the concept and nobody would argue that they need to understand the terminology as well.
The etymology of words tends to have no bearing on understanding them technically. To me, that's a non-comparison.
What's really meant is more that plenty of people use a telephone without a comprehensive understanding of EM radiation. That doesn't mean they can't use their phones, it just means if you explain EM radiation to them in terms of phones, they probably aren't going to come away understanding it any better.
First it was that, to understand, we have to "actually return to the complex terminology you're simplifying". I disagree.
Now it is, that we need some common way of communicating. I agree.
But that are two different questions.
> [explaining EM radition in terms of phones does not help]
Nor does explaining EM radiation in terms of oranges. But I'd do neither. I'd first try to figure out whether you struggle with the concept of what a phone is or with the question how it works. Because step 1 in being understood is to understand what you are trying to say, to define the metric you can later use to evaluate your success in your attempt at being understood.
Great epistemological question for the ages. Vectors for the response include audience type, previous knowledge context, goal for how much needs to be conveyed...
The same thing that it means to hear a bad quality 8bit, 20kbps copy of a song. It's still better than NOT hearing it, and it gives you an idea about what it entails, even if you don't hear all the information in it.
Even in everyday language we make the distinction about understanding something fully and having a rough understanding of it.
http://norvig.com/spell-correct.html
Norvig is a genius, and his genius is reflected in how he can so succinctly and clearly explain how to write a spell checker, without falling into elaborate jargon or droning on without getting to the point.
And that goes equally for his code and his prose, by the way.
There are many people who use a lot more jargon and verbosity to make their points, who are not in the same league as Norvig in terms of intelligence.
"The production volume of agriculturists is the reciprocal of the intellectual capacity of the producers."
also known as:
"The less intelligent the farmer, the bigger his potatoes."
That's what I hated the most with uni: Some professors could write 10 blackboards full of formulae, but could hardly put together a few words to explain what we were actually doing. Unsurprisingly, I don't remember much from these lectures. Fortunately that is not all professors, but it worries me how large a percent of them were like this.
Executing on a concept using complex technology requires complex technical terms.
ivanbakel is not making some blanket claim that things always require complex technical terms. He is just saying that language -- including field-specific jargon -- evolves so that people steeped in the language can explain things to each other.
The clearest example of that how hard it is to decypher popular articles about quantum mechanics. Here, even when explaining concepts at a skin deep level, stories they tell are utterly inadequate if not misleading.
That's because even the basic concepts of QM are ones from linear algebra. And is shy Feynman was a sometimes devotee of the "shut up and calculate" school of interpretation.
It's about explaining in a way the recipient can understand so "simple terms" becomes "terms your recipient can understand".
This is the sort of thing you'd believe if you were an arrogant 20-something who thought they could learn any subject in a few hours, cushioned thoroughly by the illusion of understanding.
"Oh yeah, I understand the mechanisms of human vision. It's just rods and cones."
"I understand the causes of the American revolution. It was just people protecting their property."
"I understand Joyce's Ulysses. It's just follows three people from Dublin over a single day. I read the Cliffs notes."
"I understand why coffee makes me alert. It's just blocking some brain things that make you sleepy."
Now, I will agree that if you don't know how to break interactions down into teachable parts, you will probably have trouble as an engineer or scientist both advancing your own knowledge and introducing people to the field. But to suggest that your understanding of a subject hinges on being able to deliver an explanation in simple terms is just silly.
For every complex system, there is usually an underlying simpler, though not accurate, model that makes grasping the broader concepts easier.
One doesn't stop at that model. (Feynman didn't.)
It's used as scaffolding, later torn down, to organize thoughts. By continuously proceeding downwards, in a fractal nature, filling in gaps, tearing and replacing where needed, the larger structure always stands ready to contextualise.
This helps hold the audience's interest. It also lets the mind, by itself, fill in gaps, promoting retention as well as pedagogical efficiency.
But I also do research, and I absolutely do not expect deeply technical topics like advances in aerospace engineering or gene regulation or cosmology to have "simple explanations" that I can understand. I accept that I won't understand them without years of effort, and I won't denigrate experts in those fields because of my limitations.
I tell people to come up with elevator pitches for complex work all the time, but I don't evaluate the quality of a thinker by the quality of their elevator pitch.
There's a difference between explaining the entire topic and just giving you a very broad strokes approach to get you started learning the subject on your own. Nobody's having any delusions about summarizing a complex subject to a few sentences to substitute learning it the hard way, but if you can't give a very gentle explanation that can ease people in to the subject so they can get started by themselves, I would say that you don't fully understand the subject.
Also, I would add that this explanation is not universal at all. You have to be able to gauge your audience and adapt to what's most suitable.
I agree cs 101 is not the world. I also agree some concepts cannot be simplified and it shouldn't.
My point was what you hinted towards when you say "distilling things down". My gripe is that most people that have taught or guided me have had no inclination to do that. I would have had a much smoother learning curve for it.
I also feel if there is a concept that can be taught by one person to another, it can be slowly be presented in increasing order of complexity than be presented all at once. That feeling of slowly building or adding complexity is underestimated and hard.
So, if you think you understand something, it's worth trying to explain it simply, so you can push your own understanding of the subject.
> To tell someone who has devoted their career to
> understanding a complex topic that they don't
> understand their subject because they can't express
> it in layman's terms without doing terrible
> violence to the underlying phenomenon is ludicrous.
No one should devote their career to simply understanding a topic. If all you do is load someone else's work into your head, what value you are adding? A career is a mixture of learning as well as exploring and discovering new things. Explaining just the parts that are known is a much smaller order than transmitting the effort of your entire career into words.
Note also that Feynman isn't claiming you should be doing this all the time, but that you should be able to. I've been programming for about two decades and I've learned a ton (and yet still have even more left to learn). I'd like to believe that, yes, I could explain almost all of it to a beginning CS student or even a lay person.
They might not have the patience for me to build up all of the necessary structure from one simple piece at a time, but I think I could. After, that's how it got into my head in the first place. The parts that I couldn't do a good job decomposing and walking through are exactly the parts that I probably don't have a good handle on. (For me, networking and operating systems come to mind. I know some of the jargon, but I don't really know how it all works.)
Complexity is real, but understanding means being able to conceptualize a system at such a high level that it becomes possible to convey the most important key ideas simply. This may involve some amount of over-simplification (which should be indicated if present) and will undoubtedly leave out a tremendous amount of detail, but the conceptual essence should be there.
The inability to do this is IMHO a sign of either lack of true and deep understanding or communication ability.
There are fields where nobody can really do this. These are fields that nobody truly understands yet.
Edit:
Let me give you an example. I had a bad (but typical) math prof in my very first calculus class who covered the board with examples and took us through how to differentiate a function. I was completely confused and stuck. Then I called my father on the phone and asked him and he told me "a derivative is a rate of change." Then I got the rest of calculus.
The prof had talked about slope but that wasn't conceptual enough. I needed "rate of change." That is the essence of calculus. It's the most important concept. Calculus deals with rates of change and the inverse (integrals). Once this concept was communicated the rest of calculus became possible to understand.
If you can't do that for a given area, you don't understand it or (as was the case with this math prof) are a poor communicator.
I suspect a so-called expert's ability to solve problems within a domain (i.e., how "expert" they are at that domain) would be a function of their ability to manipulate terms in that domain which to me is akin to their ability to those terms clearly.
I can't imagine someone easily solving problems within a domain wherein the terms they use are giant spaghetti balls of complexity. Anything can always be broken down into further levels of abstractions (or prove me wrong on that).
I think the disagreement hinges on whether you believe the snippets from the GP post e.g. the "rods and cones" or caffeine examples are fundamentally valuable or not.
> There are fields where nobody can really do this. These are fields that nobody truly understands yet.
Curious what you would consider an example of such a field?
FWIW my anecdotal example of what I think the GP is complaining about... I read "The Elegant Universe": https://en.wikipedia.org/wiki/The_Elegant_Universe
It's a good book, and I enjoyed reading it. But over subsequent years I've had growing doubts over the true value of the "understanding" that it provided.
The frontiers of physics always strike me this way. The names and explanations are incredibly strained and bizarre. This is probably the canonical example and is perhaps why The Elegant Universe doesn't quite achieve what it sets out to achieve.
Another one from my own academic past is "complexity theory" where hand-wavey concepts like "emergency" or "higher order causation" get thrown around with a lot of confusion. We can clearly see there's some "there" here, but I don't think we really understand what it all means yet. Put stuff together, interesting higher-order stuff happens, and so now let's create a combinatorial explosion of jargon around it. Publish or perish.
Finally "consciousness studies" or anything else semi-fringe probably counts. Again there's certainly some "there" there, but we don't even know the right questions to ask. Something is happening to matter that makes it wonder what's happening to it.
An important distinction to make here is whether you're teaching someone to intuitively reason about something or to logically calculate it precisely.
I think as long as someone grasps the basics of high school math and has a decent working memory, they should be able to learn how to calculate anything precisely given that you break it down into simple steps. If you don't know how to do that, you have no clue what you're doing.
Then there's intuitive reasoning. I think for most things, if you're familiar with a topic, you should be able to teach it in a way that makes sense. Of course there's exceptions -- some people are incredibly brilliant, but lack social awareness. I think that's the exception rather than the average case.
But not all topics are so easily reduced. There's probably some exceptions. The strongest that comes to mind is quantum computing. As many times as you can explain things like superdense coding, there's still a sense of "magic". Where the results of the math seem unnatural. And you go back through each step and try to figure out where things went weird. But each step is a logical progression from the beginning.
On that note, Michael Nielson's "Quantum Computing for the Determined" is one of the most well-taught courses I've found, and does a very good job of stepping the viewer through a very complicated topic. Michael Nielson clearly knows what he's doing :)
http://michaelnielsen.org/blog/quantum-computing-for-the-det...
Well, yes, if the only goal is computation. It doesn't take many instructions at all to be Turing-complete, and then you can compute everything a Turing machine can, which is lots of things.
That said, being able to calculate something can be very meaningless. You can try to do AES[1] by hand, if you'd like; it would be frustrating and very time-consuming, and then at the end of it you'll have gained effectively no understanding of its design or structure.
Using AES as a case study as well, one could explain the basic idea of encryption to a layman without too many troubles, but I can't imagine trying to explain anything about its operation or design to a layperson in a way that would make any sense at all.
[1] https://en.wikipedia.org/wiki/Advanced_Encryption_Standard#D...
Although, i would agree that some experts do a bad job of explaining things. They're still experts. I think you'd agree that non-experts don't really have a chance at explaining things.
"The limits of one's language are the limits of one's world." It's controversial, but the concept being if you can't speak about it, you really can't know it fully. This gets very fuzzy when experiencing art or emotions, but there is a cold logic to it that I appreciate, too.
Maybe, maybe, some times I'll do something clever.
Some times someone will have an insight, intuition. Like a market analysis. Or frame some useful questions for our recommenders.
Otherwise, all of the complexity that I encounter day-to-day is because of people's cognitive limitations. We make it hard. Misunderstanding, miscommunication, separation anxiety, dogma, arrogance, cya, whatever.
As an example, when we teach people how to fly a wingsuit, we essentially teach wingsuiting (which is a massively complex pursuit) as a set of nested arrays of increasing complexity.
For example, for a first jump course, the goals are as follows: - Exit safely - Demonstrate ability to navigate in-flight - Deploy
These are the most foundational aspects of flying a nylon dress out of an airplane.
After a few jumps, we'll add complexity to each of those, so to shift one point, it starts looking like:
- Exit in an unstable manner and gain stability in less than three seconds
In order to do that, you'll need to understand what causes a wingsuit to be stable, why it gets unstable, what happens when it gets unstable, and how to correct it. Additionally, you'll understand why I want you to do it in less than three seconds. However, at first, you just need to get out of the fucking plane. If I try to tell you all this extra shit you won't remember the foundational thing I need you to remember. You'll probably get unstable, you'll probably figure it out kinda, and you'll probably at some point deploy a parachute.
Teaching's hard.
I do agree that poor communication skills are not a lack of understanding, however, not being able to explain something I thought I understood is a personal redflag.
from the zen of python:
If the implementation is hard to explain, it's a bad idea.
If the implementation is easy to explain, it may be a good idea.
Everything can be talked about on different levels of abstraction, including ones which use metaphors or contain inaccuracies in order to create a jumping-off point for further learning.
If you understand something very well, you're able to use various levels of precision + abstraction in order to best communicate it to your audience. You can "play" with it, without getting confused or off-track. If you don't understand it well, this gets very hard.
I think this is true for teaching and mastery in general, and not just for teaching about science or complexity.
Nobody cares about a genius who understands something until he can really interact about the subject.
Humans work with communication. When you learn about something, you read about it and you process it. To see if you understand it, you must communicate it back. It's not really possible to guess how you brain just learned about something unless you ask that brain to reformulate it.
It's fine that it takes 150-300 hours of back-and-forth communication to transfer the ideas behind how it actually works. That seems like a reasonable amount of time to communicate a complex idea to a novice.
There's also layers of understanding:
The LHC bangs two rocks together hard to see what happens when they break.
The LHC use magnets to accelerate protons fast enough they break apart because it recreates conditions similar to the early universe.
etc.
The acceleration is actually done by electric fields produced in RF cavities.
And do you really expect politics to raise funds for such a project if nobody can explain to them what they are doing?
That's okay: politicians don't actually need to know how it works, they need to know why they should build it -- which is a) something they have domain expertise in and b) a much easier question.
That's one option. You could also apply the knowledge and see if what you think you understand has resulted in a mental model from which you can make testable predictions that correspond to the real-world behavior of the modeled thing.
It's sort of like saying that a mathematician who doesn't know how to prove their results to one who only knows the axioms doesn't fully understand their results.
I do agree it is arrogance.
> I really can’t do a good job, any job, of explaining magnetic force in terms of something else you’re more familiar with, because I don’t understand it in terms of anything else you’re more familiar with.
The article implies this is a case of the scientist expressing that he didn't understand a thing. But watching the video in full[1], one realizes he is saying something different:
"It's a force which is present all the time and very common and is a basic force.
[...]
I can't explain that attraction in terms of anything else that's familiar to you. For example if we say that magnets attract like as if they are connected by rubber bands I would be cheating you because they're not connected by rubber bands-- I should be in trouble if you soon ask me about the nature of the band. And secondly, if you were curious enough you would ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces which are the very things that I'm trying to use the rubber bands to explain. So I have cheated very badly, you see."
In other words, for some phenomena the only simple examples are themselves instances of that same phenomena. So the only possible analogies are themselves merely tautologies.
I've noticed something less sweeping though similarly absurd with the internet. As more and more of people's daily lives depend on internet technologies, it becomes more difficult to find modern, simple examples for analogies that don't rely on similar internet technologies. So someone who wants to explain the wonders of packet switching compares it to long-distance telephone calls, but they then spend the bulk of that time explaining long-distance phone calls to people who have never used a wired phone.
This actually came up for me at the office. I was asking a bunch of questions about the Z transform and the Fast Fourier Transform. The person I was talking to said, "Hey, just call the function in MATLAB, it doesn't matter how it works, just that you understand what it is saying."
All of my life I have rebelled at this notion. My earliest recollection of running into it was when I was in grade school and took apart three wind up alarm clocks, each more carefully than the one previously. My Mom was curious what I was looking for and I told her, "How does a clock know how long one second is?" She didn't know, and I didn't know, and while I had mastered using a clock and accepting that it would go off when I set it to go off, I didn't really "know" how a clock worked until I had taken apart and identified, (and modified to validate the identification :), the escapement.
Conversely, if you had to deep dive everything, you would not get _anything_ done since there's always a deeper level.
Maybe it's just an experience thing where you start to appreciate that for most things (probably all bar one or two) you are just the privileged user of other people's expertise.
My desire to understand things though has never been a hindrance to using them. Long before I understood how compilers worked I was using them daily, long before I understood how PN junctions did what they did I was soldering diodes into boards.
It only generates tension when I want some tool to do something that it cannot do, and reasoning about whether the constraint is due to the tool or the implementation of the tool can only happen if I really understand what the tool is actually doing.
The question, of course, is how well this experiment has succeeded. My own point of view — which, however, does not seem to be shared by most of the people who worked with the students — is pessimistic. I don’t think I did very well by the students. When I look at the way the majority of the students handled the problems on the examinations, I think the system is a failure. Of course, my friends point out to me that there were one or two dozen students who — very surprisingly — understood almost everything in all of the lectures, and who were quite active in working with the material and worrying about the many points in an excited and interested way. These people have now, I believe, a first rate background in physics — and they are, after all, the ones I was trying to get at. But then, “The power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous. ” (Gibbon)
Richard P. Feynman, 1963
http://feynmanlectures.caltech.edu/I_91.html
Note that by his own account, most of his students did not do well. James Gleick's biography of Feynman, Genius, has a longer discussion of the disappointing results of his lectures to undergraduates at Caltech, many of whom reportedly stopped attending the lectures as they were not getting anything useful out of them.
That Feynman in fact had difficulty explaining freshman physics to the highly qualified students at Caltech surely does not indicate he did not understand freshman physics.
Some topics are simply very complex. It is not clear that they can always be conveyed in simple terms. In some cases, a "big picture" explanation may be possible but the details remain complicated. In some cases, a hand-waving analogy to some everyday phenomenon may create the illusion of understanding but be misleading or wrong.
To give a specific modern example, a state of the art video codec such as H.264 is extremely complex, built of many complicated components and sub-algorithms. While it may be possible to explain the big picture in relatively simple terms, the detailed implementation and operation is not simple. The inability of someone who creates or implements a video codec to explain it in simple terms to a layman is not an indication that they do not understand it.
He would be proving something in class, someone would stop to ask a question, and from their question he would know not to try to answer it as asked, but rather he knew they were asking the wrong question, because the question was predicated on a misunderstanding of something three or four steps back.
Now these were proofs that a working mathematician could probably do in their sleep, but they were a level up in terms of abstraction for most of the students and to be able to drag us along with him was a rare talent.
We now have programs that "understand" certain domains better than humans. And yet there are no "simple terms" to explain their understanding, reduce it to a neat closed-form formula.
Isn't it a mistake to assume a nice, elegant explanation, a cute human "narrative", must always exist?
"But Radim, the computers don't really understand the domain!". Sorry, a cop out, No True Scotsman fallacy. In what way do they not?
This is crystal clear with Go: the little stories humans have built to deepen their understanding of the game over 2,000 years are irrelevant to a game's outcome. The details and variations are all that matters, and there is no way to reach the computer's level of understanding of the game without understanding the details.
Even after I got my undergrad degree in physics I would reread the Lectures and would see things on a whole new level than I ever understood them the first time.
Edit: even "Surely you're Joking" had jokes that only someone that had graduate level general relativity would get (talking about "gee-mue-nue, gee-mue-nue")
Some people look at advanced mathematics or physics and wonder why it has to be so complicated and so full of jargon. It's complicated because it is. The jargon, believe it or not, is mostly an attempt to make it easier to communicate. It would be very, very difficult to wade through these ideas without introducing new words with precise definitions.
Then again, John von Neumann said, "In mathematics you don't understand things. You just get used to them." So maybe the title is true for trivial reasons after all.
He was not talking about writing a research paper on the simplest possible terms. Rather, about "explaining" a subject. When we are explaining, we always have to deliberately omit details to get the basic idea across, so that the other person can form the initial mental image. Sometimes we also have to resort to metaphors and comparisons from entirely different fields, or relate them to real world concepts.
Once that is done, then the lengthily process can begin on improving the fit of that mental image to the subject. This will require more explanations, more focused, in a different level of detail.
Case in point: dimensions higher than three. Most people cannot conceive what the heck a tesseract is, or why it is usually drawn the way it is. But then you can tell them to watch Feymann's Flatland scenario, and they will be able to understand the basic concept.
Are they mathematicians now? Hardly. But now they have some understanding on the subject which they did not have before, even if it is on a very high level. And can try to absorb more details, if so inclined.
I would tentatively agree that there is a skill which allows you to break down complex subjects into digestible chunks, but that usually depends a lot on the student as well as the teacher(e.g. some people are good at following metaphors, others learn very well from repeated examples, etc), but the outright statement in the topic suggests that there is no such thing as irreducible complexity, which seems ludicrous.
Nobody's having any delusions that explaining is the same as teaching. You can explain multidimensional analysis simply if you understand the subject fully, however you can't teach something to someone else unless they work with you and try it out themselves.
But if you want to explain to your politicians that hospitals need special machines to do radiation therapy you don't enroll them into nuclear physics 101, they can probably do with a very broad explanation of how radiation works.
Maybe explaining a complex concept in simple terms would take you 2 hours, 12 hours or 3 days, but you can do it if you really understand it.
It is also dangerous to assume this, because that is exactly how we reached the "my uninformed opinion is as valid as your years of experience" aspect of the current political climate. NO, things are NOT as simple as you think they are just because you saw it in the space of a tweet!
On the other hand, it is important to recognize expertise over bullshit. The easiest defense is having several experts, since at a certain point they would need to do an awful lot of collusion to just make things up between them (i.e. if enough of them agree then what they say is apparently correct).
This is just to get people started, it's not a substitute for years of hard work and study. Feynman never claimed this and I think this is missing the point entirely. Unless you have a complete model of how the system works you can't come up with suitable analogies to gently ease in new people to get started.
It's at least more correct than someone with zero training in that field. Dissenting opinions among experts should also be considered, by such experts, and the points at which they disagree with the logic or knowledge carefully examined by all.
And there are three kinds of explanation:
1. visual
2. mathematical
3. linguistic
So sometimes, you understand something visually, or mathematically, but you are forced to put it into verbal terms (say, over a text only channel, or voice), and then you may seem not to be able to explain it even though you understand it.
http://scottmccloud.com/4-inventions/triangle/index.html
http://homes.chass.utoronto.ca/~mfram/Media/0505-UC-triangle...
Filed under "I believe, but cannot prove": The three-way tension is a recurring pattern.
When trying to understand new things, I often try to reframe things as a triangle. When pondering intractable problems, I favor three-way solutions. Some quick examples from memory...
Project management: time, money, scope.
aka Quality: Fast, good, cheap.
US Govt balance of power: Executive, Congress, Judiciary
Language design: imparative, declarative, functional
Pop music: harmony, melody, lyrics
If you have to budget something, it becomes a soft trilemma: I have 24 hours for work + leisure + sleep, so any given combination will be a point inside a triangle whose vertices are (0, work), (0,leisure), (0, sleep). This structure is called a (2-)simplex.
BTW: a regular dilemma (should I spend or save) is a 1-simplex, and is a simple linear combination asave + (1-a)spend.
Now, this is fun for two reasons:
- You can have (n)-lemmas (i.e. n-fold tradeoff structures) that are modeled as (n-1)-simplices. Actually useful: you can do statistical inference on simplices using the Dirichlet distribution.
- A simplicial complex (basically, a set of simplices) can be used to build topological spaces part by part. This kind of maths (algebraic topology) is a whole "south part of the mountain" climb towards abstract mathematics that bypasses a lot of Cantorian handwringing on the ultra-local structure of topology. Instead, you're computing stuff from the get go -- and indeed one of the emerging machine learning techniques goes precisely from building a simplicial-like complex from data and computing characteristics of its topology.
Next time I see this concept in action, maybe I'll suggest alternate methods of "explaining".
I'm not saying I'll take it as literally true in every situation. But what I love about the quote is that it sets the bar for "understanding" very high.
People sell themselves short on understanding - they reach a certain level and are satisfied that they understand something, when there is actually much deeper understanding to be had. For example, being able to write a proof of a theorem can be very far from understanding why it's true, but even mathematicians sometimes pretend it's the same.
So I like that this quote challenges us to understand things more deeply. And more often than not, I find it rings true.
(A basic example coming to mind is the determinant of a matrix. Can be explained in simple terms to children (at least the key idea), or in confusing terms to freshman linear algebra students....)
I think the effort involved in trying to come up with a serialization causes us to more carefully examine our models, which usually improves them.
But I don't think the lack of a good serialization implies the lack of a good model.
Explaining something in simple terms does not mean you _fully_ explain it. You explain the essence (or what you see as the essence) of the thing. Google search is: you type a question into a box and Google shows you the best answer. Google search is a lot more than that, of course, but if you can't "boil it down" you don't understand it.
This is the top line of a git commit v.s. the comments you leave in the source code. You can spend months working on thousands of lines of code, bur if you can't describe it in a single sentence (while leaving a lot out!) it's a bad sign.
It is amazing how rarely people can get it across to me in basic terms. In fact even the idea of breaking it down into non technical concepts seems to be surprising and alien to many people.
I really admire those who can.
The Feynman Lectures are now on Youtube[0], and I like to watch them (all of them) every few years. I highly recommend that if you've never seen them, you take some time and watch them- really watch them. Close the other windows, turn your phone to do not disturb, and really watch these masterpieces of education.
You link to: https://en.wikipedia.org/wiki/The_Character_of_Physical_Law
"Feynman Lectures on Physics" are: https://en.wikipedia.org/wiki/The_Feynman_Lectures_on_Physic...
Are you serious?!?!
Oh shit, that's... I've been grossly misformed for a very long time.
And in my experience, the harder the subject, the more informally experts speak. Partly, I think, because they have less to prove, and partly because the harder the ideas you're talking about, the less you can afford to let language get in the way.
Informal language is the athletic clothing of ideas.
I'm a physicist, and if you asked me to explain Newton's laws or classical thermodynamics to someone, I could probably give them a reasonably complete overview in a few hours. And in doing so I'd probably introduce and explain some jargon (entropy, derivatives, etc) along the way to make it easier.
On the otherhand, if you asked me to explain Quantum Field Theory or General Relativity in the same time, I'd basically just give up and throw out some friendly but inexact analogies about stretched rubber sheets and the like, and hope the walked away with some vague sense of the outlines of the subject.
I think PG has confused the informality people have when they have a common understanding with something else. Do you really think that a pair of experienced mechanics in an auto shop discussing a basic repair are going to be using more formal language? Turn one of the mechanics into an apprentice and consider the same discussion.
It doesn't work for biology, which is complicated at the bottom. Evolution doesn't have the parsimony of physics. Nor does it have to be understandable by humans.
Whether it works for software is a design issue. It's certainly possible to create software which cannot be explained simply.
(I'm actually really hoping for someone to show up and say, "Um, gosh, I don't know how to say this, but that's just so wrong..." And then how.)
This incompatability has caused me problems my entire career. I've more or less stopped trying. I just do what I'm told and save my creative energy for my personal projects.
And an underappreciated corollary is...
If you want something explained well in simple terms, you have to find someone who understands it deeply.
In the sciences, that means someone who has it as their research focus. Because as you move away from that focus, understanding rapidly becomes ramshackle. Leave someone's subfield, and you might as well be talking with a random graduate student (in that field). And that's hopeless.
Thus many research talks have videos and stories which would nice to have in a K-12 classroom. And most all K-12 education content is incoherent wretchedness.
An old essay of mine: "Scientific expertise is not broadly distributed - an underappreciated obstacle to creating better content" http://www.clarifyscience.info/part/MHjx6 In which a 5-year old with finger paints wants to paint the Sun, but encounters astronomy graduate students.
"I am sorry for the length of my letter, but I had not the time to write a short one." - Blaise Pascal 1657
There's a sad little genre of low-quality science education research that goes: "I tried to teach topic T to students of age A. I taught it <really really badly>. Surprisingly, that didn't work! I've reach the obvious conclusion: students of age A are developmentally unready to learn topic T."
But understanding, while necessary, is not sufficient. At PhD poster session practice, it's often remarkably hard to help candidates develop an "elevator pitch". To clearly understand the core of what they've spent the last n years working on. I'm still amazed by how often one gets something like "wow, now I can explain it to my parents".
"But if you can ONLY explain something in simple terms, you still don't understand it"
For example, a lever seems conceptually simple, but to create a lever in the body is extraordinarily hard. The joints have to be solidly connected and free to open or close. The direction must be precise and rotation must not wobble. There are so many things that can err and lots of places for force to leak out.
I think there are too many times when people affect a tone of authority and expertise and hide their lack of understanding in verbiage and complexity while making excuses for their inability to explain it to the layman.
Many think they understand something, when really they only know how to use it. For example, I understand how to use a computer, but that doesn't mean I understand how a processor works at the level of registers and assembly language. So if I were to try to teach someone a computer, then I could say things like "Click that, and this will happen," or "Type such and such, and then this other thing you want will happen." But if anyone asked me about how that actually works, to follow all the way how a physical mouse-click gets transformed into a change in the window on the screen, then I couldn't. Or, even if I could, it might take me half an hour to explain it, depending on how much they want to know.
So maybe it's that we undestand things, but at different levels. Few people understand something at its deepest level. In fact, physicists would say no one does.
Monkey eat => Monkey live.
Monkey live => Monkey eat.
Monkey not eat => Monkey not live.
Monkey not live => Monkey not eat.
Here "=>" is used as in "implies"/"because". The last statement is weird. There are more ways for monkey to "not live" than to "not eat".
Not being able to explain does not imply not being able to understand. Not understanding surely implies not being able to explain.
Correlation, Causation, get it ?
A statement like "if not a, then not b" is not applicable unless a "implies" b and a "is because of" b.
Correct me if I got it all wrong somehow.
The Buddha and the Upanishadic seers were exceptionally good with explaining complex phenomena in simple terms.
Apparent sophistication is a sign of a confusion. Clarity is an evidence [of deep understanding].
Nature is vastly complex but not complicated (a few fundamental laws at work). Only simple things work.
Edit: nevermind. I was way off.
Ce qui se conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément.
If you can't explain it to a six year old, you don't understand it yourself.
https://www.goodreads.com/quotes/19421-if-you-can-t-explain-...
Often, it takes a lot of awareness of what are the common mental models / mental blocks other people have when learning the concept you are trying to communicate. You have to structure things as a series of strategic progressions before tackling the most complicated form of something, all of that is more the art of teaching ( which of course requires good understanding )
Of course, if someone can do that, it's a brilliant proof they do understand something.
If they can't do it, then it can leave you with doubt what someone else understands. Which in Apples case may be considered entirely unacceptable.
The main issue when explaining concepts (especially maths concepts) is switching from one formal context to another, deciding what details to omit, and determining what rules in both contexts should be treated as analogous.
Think of a translator. He/she/it needs proficiency in two languages to do a proper translation. Lacking a second language precludes translation. But it doesn't affect mastery of your native tongue.
A popular question to qualify for engineering job interviews is "describe in simple terms what happens when a user accesses a website on the Internet" - The question doesn't give any info on who the target audience is so you never know what level of detail you're supposed to go into. Because this is an engineering question, I tend to go into more detail but after a certain level, you can't really keep it simple because the reader has to understand what things like cache are... Else you will spend 20 pages just writing definitions.
Skeptic: “I understand X. I’ve spent years working on it, and I’m recognized as an expert in the field. but I can’t explain X in simple terms.”
Believer: “Well, then you obviously don’t really understand it. Can you prove to me that you do"
Being able to explain things in simple terms is a skill in and of itself. Many people do not possess this particular skill, but that does not mean they are unable to understand any subject.
She'd gone to Caltech. That was on her resume. So I asked her if she'd ever taken a class from Feynmann. That was actually unlikely but she had sat in on a seminar with Feynmann once. She said he could explain the most difficult material and that you would understand it. You would understand it walking away and this would last about 15 minutes during which time you confuse yourself.
Eg. IP = A address like your home address. So the internet knows where to search. We use zipcodes, the web uses numbers.
Then: I need to adjust a dns-record with our IP. Becomes, I will point the website to our address.
If it's not obvious, then all my previous clients are lying ( just mentioning it, cause it's possible)
Sadly it's 2017 and the popularity of TEDTalks make the laymen think otherwise.
Take for example legal concepts like securities law or environmental regulation. Yes, you can "simplify" an explanation of the Securities Act or the Paris Accord enough to fit them into a tweet, but you lose information necessary to formulating a full understanding.
If you're trying to have an informed debate about policy adoption, the details matter.
Opposite example: Simplify how walking works, and make sure to include the critical systems such as major muscle groups, stabilizers, vision, inner ear, thigh/knee/pelvis/hip construction, the curved spine and its connection to the head, and blood pressure flow/regulation.
You'd be missing a lot of experimental data that has been collected for decades. You'd be missing the metallurgy, etc.
The basic principle is very simple. Maybe you could even build a low powered version, given materials and time.
If you insist that understand how to obtain the proper air to fuel ratio is required to understand how an internal combustion engine operates, then I'd say we don't really understand anything at all. Can you mine and refine the ore to create the allows it is made of? Can you program the ignition (or alternatively, build a carburator)?
We all need to stop at some point.
Take it a step further and the engine is built, but you need to make a modification (forced induction, race fuel, etc). If you don't want your engine to blow up, now you need to understand air/fuel mixture. Sure, I can do something with a simplified understanding. But the lack of a complete understanding will leave me with a blown-up engine.
Does it follow that if I understand metallurgy and internal combustion engines, but can't simplify it, that I don't understand it? Of course not; the entire premise was that I already understood it. Simplification does not show you understand something. It can only provide a shallow, incomplete understanding.
So you don't need to be able to simplify to understand. You need to understand to understand. You need to simplify to provide a simplistic, shallow view.
https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theore...
And to be fair, it's pretty rough sledding even when you understand the operators involved.
If you hold a complex idea in your head translating that into English can be difficult because part of the process is removing/altering information to fit into existing notions. That is why buzzwords are popular they can take an idea and put it in a relatable concepts for the masses.
In fact, "if you make this fallacy, you're a terrible human being" (which is sarcasm here since this very statement includes the exact same fallacy)
1. be familiar to the logical reasoning : what «implies» or even «for any x» means. 2. know the relevant set of theorem and axioms used in the demonstration.
You could probably illustrate what a mathematical result implies in some real-life example, but you won't be «explaining» it.
Quantum physics is a really good example of this, because it's not that difficult to understand if you look at it with the mathematical PoV : it's basically linear algebra in infinite dimension, you have vectors (in the space of «functions of |R³») and linear applications on these vectors (with all properties of such applications, like eigenvalues and eigenvectors), etc. But if you try to «explain» it in simple terms, you're going to distort the reality to fit in the macroscopic-scaled human representation of the world and you'll probably say things that won't be true.
So, no, you cannot explain everything in simple terms. But you can find sweet spots when trading brevity for accuracy.
I understood very early in life that if I cried I would be hit. I couldn't talk, write, or communicate my understanding in any way, but I understood clearly.
Whatever is well conceived is clearly said, And the words to say it flow with ease.
Ce que l'on conçoit bien s'énonce clairement, Et les mots pour le dire arrivent aisément.
Remember that "in simple terms" does not mean easy or over simplifying something. To me it means making a to-the-point and jargon-free explanation.
I've witnessed dozen of people try and spectacularly fail at teaching their own language.
:-P
[1]: https://stackoverflow.com/questions/9452701/ukkonens-suffix-...
In the words of the xkcd on the subject, (check the title text):
"Actually, I think if all higher math professors had to write for the Simple English Wikipedia for a year, we'd be in much better shape academically." https://xkcd.com/547/
At least, that's the programmer's interpretation. Mathematically, they are algebraic structures that can behave analogously to this in a number of fashions.
We've started doing Explorable Explanations / Animated Explainers, here are some we've done and some that others have done:
- Explaining how GIT works: http://gun.js.org/explainers/school/class.html
- How neurons work: http://ncase.me/neurons/
- How end-to-end cryptography works: http://gun.js.org/explainers/data/security.html
- How gerrymandering works: http://polytrope.com/district/ (by a friend of mine!)
- How sorting on partial data / data streams works: http://gun.js.org/explainers/basketball/basketball.html
And more! It is possible, it can be done. But it is hard. That is no excuse for not trying though. Big shout out to Bret Victor's work for starting a lot of this, and thanks to Feynman for encouraging and practicing what he teaches.
Person B: How?
Person A: You're a dummy! There's mountains of evidence!
Person B: Like...
Person A: You're killing the vibe brah.